$\dfrac{ 9t - 9u }{ 10 } = \dfrac{ 5t - 3v }{ -9 }$ Solve for $t$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 9t - 9u }{ {10} } = \dfrac{ 5t - 3v }{ -9 }$ ${10} \cdot \dfrac{ 9t - 9u }{ {10} } = {10} \cdot \dfrac{ 5t - 3v }{ -9 }$ $9t - 9u = {10} \cdot \dfrac { 5t - 3v }{ -9 }$ Multiply both sides by the right denominator. $9t - 9u = 10 \cdot \dfrac{ 5t - 3v }{ -{9} }$ $-{9} \cdot \left( 9t - 9u \right) = -{9} \cdot 10 \cdot \dfrac{ 5t - 3v }{ -{9} }$ $-{9} \cdot \left( 9t - 9u \right) = 10 \cdot \left( 5t - 3v \right)$ Distribute both sides $-{9} \cdot \left( 9t - 9u \right) = {10} \cdot \left( 5t - 3v \right)$ $-{81}t + {81}u = {50}t - {30}v$ Combine $t$ terms on the left. $-{81t} + 81u = {50t} - 30v$ $-{131t} + 81u = -30v$ Move the $u$ term to the right. $-131t + {81u} = -30v$ $-131t = -30v - {81u}$ Isolate $t$ by dividing both sides by its coefficient. $-{131}t = -30v - 81u$ $t = \dfrac{ -30v - 81u }{ -{131} }$ Swap signs so the denominator isn't negative. $t = \dfrac{ {30}v + {81}u }{ {131} }$